Saturday 22 September 2018 |

Events for day: Tuesday 02 January 2018 |

09:00 - 10:00 LectureProny's Method for Multivariate Exponential Sums School MATHEMATICS Prony proposed 1795 a method to solve the parameter reconstruction problem for exponential sums in the univariate case. The key idea is to consider an associated polynomial equation and to study an equivalent algebraic problem. In this talk, we present a generalization of Prony?s method to the multivariate case. We discuss related algebraic problems and methods. The talk is based on joint work with Stefan Kunis, Thomas Peter and Ulrich von der Ohe. ... 11:00 - 12:00 LectureCastelnuovo-Mumford Regularity (II) School MATHEMATICS In this lecture, I will give some basic properties of the Castelnuovo-Mumford regularity and its applications to bound Hilbert coecients. 1. Denition and some basic properties In this part, I will give the denition of the Castelnuovo-Mumford regularity by using local cohomology. Then I will recall basic properties such as Castelnuovo's lemma and the relation of the Castelnuovo-Mumford regularities of modules in an exact sequence. 2. Characterization of the Castelnuovo-Mumford regularity by syzygies The main focus of this part is to present Mumford's characteri ... |